World of ultracold atoms wiWorld of ultracold atoms with strong interaction th strong interaction

National Tsing-Hua University

Daw-Wei Wang

Temperature ?

What we mean by “ultracold” ?

610 K !T

Why low temperature ?Why low temperature ?

x p

Therefore, if TT

2

~ ~ ~ , Thermal wavelength2 2

B T

B

pk T x

m p mk T

Ans: To see the quantum effects !

Uncertainty principle:

1/3Quantum regime when ~T d n

dT

(after Nature, 416, 225 (’02))

Why strong interaction ?Why strong interaction ?

Because interaction can make “many” to be “different” !

P. Anderson: “Many is not more”

Example: 1D interacting electrons crystalization and no fermionic excitation

How to make interaction stronger ?How to make interaction stronger ?

N

jiji

N

jj

j xxUxVm

H )(2

1)(

21

2p

smaller becomes or smaller becomes ~ .2 mTkE Bk

dimensionlower make tochanges )( .3 xV

stronger becomes )( .1 xU

ninteractio range longfor smaller

n);interactioshort (for larger becomes .4 N

How to reach ultracold temperature ?How to reach ultracold temperature ?

1. Laser cooling !(1997 Nobel Price)

Use red detune laser+ Doppler effect

How to reach ultracold temperature ?How to reach ultracold temperature ?

2. Evaporative cooling !

Reduce potential barrial+thermal equilibrium

Typical experimental environmentTypical experimental environment

MIT

How to do measurement ?How to do measurement ?Trapping and cooling

Perturbing

Releasing and measuring BEC

(2001 Nobel Price)

What is Bose-Einstein What is Bose-Einstein condensation ?condensation ?

Therefore, for fermion we have ( , ) 0,

i.e. fermions like to be far away,

but bosons do like to be close !

x x

1 2 2 1( , ) ( , ), + for boson and - for fermionx x x x

When T is small enough,noninteracting bosonslike to stay in the lowestenergy state, i.e. BEC

How about fermions in How about fermions in T=0 ?T=0 ?

When T-> 0, noninteracting fermions form a compact distribution in energy level.

E

D(E)

Fermi sea

BEC and Superfluidity of bosonsBEC and Superfluidity of bosons

Superfluid

Normal fluid

v repulsion

Landau’s two-fluid model

BEC = superfluidity

uncondensate

condensate(after Science, 293, 843 (’01))

Phonons and interference in BECPhonons and interference in BEC

m

Unvph

0

Phonon=density fluctuation Interference

Matter waves ?

(after Science 275, 637 (’97))

Vortices in condensateVortices in condensate

extln lnnlnlE 20, 223

Vortex = topological disorder

E

L1 320

Vortices melting, quantum Hall regime ?

(after Science 292, 476 (’01))

(after PRL 87, 190401 (’01))

Spinor condensation in optical trapSpinor condensation in optical trap0,1,1 FmF

JIF

Na

B

EF=2

F=1

lklkjijiijjiii

gg

mdH ˆˆˆˆ

2ˆˆˆˆ

2ˆ

2ˆ 20

2

FFr

(see for example, cond-mat/0005001)

Boson-fermion mixturesBoson-fermion mixtures

Sympathetic cooling

Fermions are noninteracting !

phonon-mediated interaction

fermion

phonon

E

D(E)

Interacting fermi sea

rf-pulse

NaLiLiLiRbK 236768740 or , ,

Feshbach ResonanceFeshbach Resonance(i) Typical scattering:

(ii) Resonant scattering:

0

0 1BB

Baa

B

a

Molecule state

Molecule and pair condensateMolecule and pair condensate

(JILA, after Nature 424, 47 (’03))

K40

(MIT group, PRL 92, 120403 (’04))

Li6

(Innsbruck, after Science 305, 1128 (’04))

2/9,2/9

2/5,2/9

2/5,2/9

2/9,2/9 2/7,2/9

B

a

First evidence of superfluidity of fermion pairing

Optical latticeOptical lattice3D lattice 1D lattice

Entanglement control 22

2

0

)(

E

EV R

other lattice

E

Mott-Insulator transitionMott-Insulator transition

i

iii

iiiiji

ji aaaaaaUaatH )1(,

(after Nature 415, 39 (’02))

Ut /

n=1

n=2

n=3 superfluid

Bose-Hubbard model

Fermions in optical latticeFermions in optical lattice

i

iiji

sjsi nnUaatH ,,,

,,

Fermi Hubbard model

Superfluidity of fermion pairing in lattice is also realized.

Transport in 1D waveguideTransport in 1D waveguide

Interference ?

Finite temperature+ semiconductor technique

wave guide

wire

Dipoles in nature:Dipoles in nature:(1) Heteronuclear molecules (2) Atoms with large

magnetic moment

(a) Direct molecules p~ 1-5 D (b) But difficult to be cooled

Cr)(for 6~ BSmall moment

nK1~ U,1 ,K10~ U1D,~p ddBdd

But it is now ready to go !

(Doyle, Meijer, DeMille etc.) (Stuhler etc.)

Condensate (superfluid)Condensate (superfluid)

Tc~700 nK

B6

Cold dipolar atoms/moleculesCold dipolar atoms/molecules(1) Heteronuclear molecules (2) Atoms with large

magnetic moment

(a) Direct molecules p~ 1-5 D (b) But difficult to be cooled

Cr)(for 6~ BSmall moment

nK1~ U,1 ,K10~ U1D,~p ddBdd

But it is now ready to go !

(Doyle, Meijer, DeMille etc.) (Stuhler etc.)

Condensate (superfluid)Condensate (superfluid)

Tc~700 nK

B6

Interdisciplinary fieldInterdisciplinary field

Ultracold atoms

TraditionalAMO

Quantum Information

NonlinearPhysics

Precise measurement

Condensed matter

Cosmology

Soft-matter/chemistry